Question

Construct ${75}^{\circ }$ and verify by measuring it by a protractor. [3 MARKS]

Answer 1

Steps : 1 Mark
Construction : 2 Marks

Steps :
1. Take the given ray PQ . Draw an arc of some radius taking point P as its centre, which intersects PQ at R.
2. Taking R as centre and with the same radius as before , draw an arc intersecting the previously drawn arc at S.
3. Taking S as centre and with the same radius as before, draw an arc intersecting the first arc at T.
4. Taking S and T as centre, draw an arc of same radius to intersect each other at U.
5. Join PU. Let it intersect the initial arc at V. Taking S and V as centre, draw arcs with radius more than $\frac{1}{2}SV$.
6. Let those intersect each other at W(as shown in figure). Join PW which is the required ray making ${75}^{\circ }$ with given ray PQ.

The angle so formed can be measured with the help of a protractor. It comes to be ${75}^{\circ }$